# Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions

*2022, Volume 27, Number 1, pp. 43-64*

Author(s):

**Chenciner A., Sauzin D., Sun S., Wei Q.**

We address the following question: let
$F:(\mathbb {R}^2,0)\to(\mathbb {R}^2,0)$ be an analytic local diffeomorphism defined
in the neighborhood of the nonresonant elliptic fixed point 0 and
let $\Phi$ be a formal conjugacy to a normal form $N$. Supposing
$F$ leaves invariant the foliation by circles centered at $0$, what is
the analytic nature of $\Phi$ and $N$?

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